Answer:
(x^2 + 7) (x^4 - 7 x^2 + 49)
Step-by-step explanation:
Factor the following:
x^6 + 343
Hint: | Express x^6 + 343 as a sum of cubes.
x^6 + 343 = (x^2)^3 + 7^3:
(x^2)^3 + 7^3
Hint: | Factor the sum of two cubes.
Factor the sum of two cubes. (x^2)^3 + 7^3 = (x^2 + 7) ((x^2)^2 - 7 x^2 + 7^2):
(x^2 + 7) ((x^2)^2 - 7 x^2 + 7^2)
Hint: | Evaluate 7^2.
7^2 = 49:
(x^2 + 7) ((x^2)^2 - 7 x^2 + 49)
Hint: | For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^2)^2.
Multiply exponents. (x^2)^2 = x^(2×2):
(x^2 + 7) (x^4 - 7 x^2 + 49)
Hint: | Multiply 2 and 2 together.
2×2 = 4:
Answer: (x^2 + 7) (x^4 - 7 x^2 + 49)
